Optimal Portfolio-Consumption with Habit Formation and Partial Observations: The Fully Explicit Solutions Approach

Details Optimal Portfolio-Consumption with Habit Formation and Partial Observations: The Fully Explicit Solutions Approach Optimal Portfolio-Consumption with Habit Formation and Partial Observations: The Fully Explicit Solutions Approach

2011-12-13

arxiv.org/abs/1112.2939v2

Economy

Quantitative Finance

Portfolio Management

27 pages

Scientific paper

We consider a model of optimal investment and consumption with both habit-formation and partial observations in incomplete Ito processes markets. The individual investor develops addictive consumption habits gradually while he can only observe the market stock prices but not the instantaneous rates of return, which follow Ornstein-Uhlenbeck processes. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated HJB equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We will provide the optimal investment and consumption policies in explicit feedback forms using rigorous verification arguments.

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